How to Lie With Statistics in the Atlantic Monthly

I promise to comment on James Fallows' real important article
on the War on Terror in the current Atlantic Monthly
real soon now. But on my way, I noticed … well, a blast
from the past there on pages 36 and 37, in an article titled
"The Heights of Inequality" by Clive Crook. You can read the first two
paragraphs (or the whole thing, if you're a subscriber like me) here.

In 1971, Jan Pen, a Dutch economist, published a celebrated treatise
with a less-than-gripping title: Income Distribution. The book
summoned a memorable image. …
Suppose that every person in the economy walks by, as if in a
parade. Imagine that the parade takes exactly an hour to pass, and that
the marchers are arranged in order of income, with the lowest incomes
at the front and the highest at the back. Also imagine that the heights
of the people in the parade are proportional to what they make: those
earning the average income will be of average height, those earning
twice the average income will be twice the average height, and so on.
We spectators, let us imagine, are also of average height.

Pen then described what the observers would see. Not a series of
people of steadily increasing height—that's far too bland a picture.
The observers would see something much stranger. They would see,
mostly, a parade of dwarves, and then some unbelievable giants at the
very end.

Why did I consider this a blast from the past? Because back when I was
a young'un, I read a great little book by Darrell Huff: How to Lie With
Statisics. And one of his examples of
chicanery was exactly
the method used by Pen, now echoed by Crook.

Suppose, Huff said, we want to
represent the difference in incomes between Rotundia ($30/week) and
America ($60/week). (The book was written back in 1952.)
We could draw a bar graph (and Huff does), but
that's pretty boring. We could also (and Huff does) draw a picture of an
American holding two moneybags and a Rotundian holding one:

That's fair. But let's not be fair; let's lie.
Huff draws a graphic with two
moneybags, the American's twice as tall as the Rotundian's:

Now, Huff points out, the heights of the two moneybags are in two-to-one
ratio; but
the actual area of the American's moneybag on the printed page (or, in
our case, the screen) is four times
bigger. Worse (or, if we're doing the lying, better), the mind's eye is
busy imagining the actual 3-D object, which, being twice as large in every
dimension, is actually eight times bigger.

And this is how Pen lied, and how Crook lies in echoing him.
The "unbelievable giants" we're asked to imagine at the end of the
parade really are unbelievable; they are the equivalent of
the American's moneybag above.

It would be bad enough if this were just done in words, but the
Atlantic graphics folks actually have a cute drawing of the
parade across the two-page spread with the "unbelievable giants"
(or the shoe of one of them, anyhow) at the right edge. In short,
the Atlantic actually redoes Huff's big-moneybag illustration.

Now the article is not without its points. I just thought it was cute
how a 2006 article quotes a 1971 treatise, both enthusiastically using a
dishonest technique debunked in 1952. Nothing new under the sun.

I'd suggest the Atlantic
buy copies of How to Lie With Statistics for its entire editorial
staff. (The Amazon page is here. If
you don't want to buy the book, cheapskate,
you can "search inside the book" for "moneybag" and read
Huff's funny exposition, it's classic.)

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